Question: An object is launched from a platform. Its height (in meters), $x$ seconds after the launch, is modeled by: $h(x)=-5x^2+20x+60$ How many seconds after launch will the object land on the ground?
Explanation: The object hits the ground when $h(x)=0$. $\begin{aligned} h(x)&=0 \\\\ -5x^2+20x+60&=0 \\\\ x^2-4x-12&=0 \\\\ (x+2)(x-6)&=0 \\\\ \swarrow &\searrow \\\\ x+2=0\text{ or }&x-6=0 \\\\ x=-2\text{ or }&x=6 \end{aligned}$ We found that $h(x)=0$ for $x=-2$ or $x=6$. Since $x=-2$ doesn't make sense in our context, the only reasonable answer is $x=6$. In conclusion, the object will hit the ground after $6$ seconds.